C₃₇×#3455 #17992273

order	4736
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₃₇ · Schur multiplier (H₂) = C₂⁸

Aliases

direct product

C₃₇×#3455

Subgroups

	subgroup	G/H
center	C₂×C₄×C₃₇	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁵×C₃₇
socle	C₂²×C₃₇	C₂⁵
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₃₇ ◁ G

1040 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 61
transitive degree	μ_t(G) = 1184

A minimal faithful permutation representation — 5 generators on 61 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37)(38,39)(40,42)(41,43)(44,45)(46,47)(48,54)(49,53)(50,52)(51,55)(56,60)(57,59)(58,61);(38,40,41,44)(39,42,43,45)(46,48)(47,51)(49,56)(50,55)(52,54)(53,58)(57,61)(59,60);(39,43)(42,45)(48,55)(51,54)(56,61)(58,60);(47,52)(51,54)(53,59)(58,60);(46,49,50,57)(47,53,52,59)(48,56,55,61)(51,58,54,60)

Conjugacy classes & character table

1628 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃₇×#8411, C₃₇×#12720, C₃₇×#18126, …
maximal normal subgroup of	C₃₇×#8411, C₃₇×#12720, C₃₇×#18126, …
maximal quotient of	C₃₇×#34048, C₃₇×#34056, C₃₇×#34065, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 2187);

C37×#3455 #17992273